Such funds held $2.659 trillion at last count, according to the Investment Company Institute. They offer better rates, normally, than certificates of deposit and money market accounts but come with no FDIC insurance.

That’s because money market funds are mutual funds rather than bank accounts. However, they are deemed safe because they are generally required to invest in short-term debt such as U.S. Treasurys and commercial paper.

Investors use them to park money they intend to invest elsewhere and often prefer the liquidity they offer, as well as the slightly higher returns compared to guaranteed deposits.

Nevertheless, Schapiro said she is worried. “I do feel a sense of urgency about the structural weaknesses that exist in money market funds,” Shapiro said a breakfast with reporters sponsored by the Christian Science Monitor.

She also worries about a repeat of the Flash Crash of May 6, 2010, she said. During that event, the Dow plunged 1,000 points in seconds before recovering a few minutes later.

Money market funds rarely stiff their shareholders, but it can happen. In 2012, the Reserve Primary Fund had to report losses on Lehman Brothers debt it held when that institution went under. Investors panicked and demanded their money, feeding a collapse of the fund. The SEC sued the money market fund for failing to provide material facts to its investors or misleading them. In the end, investors recovered 98 cents on the dollar, after the agency’s intervention.

Schapiro specifically mentioned the ongoing problems in Europe as context. SEC moves after the Lehman debacle “clearly helped these funds weather a lot of the volatility of the European crisis this (past) summer,” she said.

Greece has managed to push off its potential default for a while longer, thanks to round-the-clock negotiations with the European Union. The latest deal is the second rescue in three years, but not everyone is convinced it will stick.

There was some fear earlier this year that a run on European banks would spread abroad, hurting U.S. banks and causing investors to stampede out of money market funds, a replay of the 2009 credit crunch that took down Lehman and Bear Stearns.